First, she isn't going to get convicted. Those laws are written for people that are spies or that intentionally give away secrets. They simply do not apply to someone that is stupid and does something stupid.
That said, if she gets convicted she can still serve. Unless the House impeaches her (which means bring charges) and the Senate would then have a trial on those charges and if convicted she would be removed from office.
It would never come to that, if convicted she would cut a deal with her VP to be pardoned if she resigns. Just like with Nixon.
But again, she isn't going down for the emails.